A method for adaptively separating echo signals of a target body and a micro-motion component

Abstract

The application particularly relates to a method for adaptively separating echo signals of a target main body and a micro-motion component, and belongs to the field of radar signal processing, which comprises the following steps: firstly, based on the low-rank property of the time-frequency representation of the echo signal of the target main body and the sparsity of the time-frequency representation of the echo signal of the micro-motion component, the separation problem of the echo signals of the target main body and the micro-motion component is modeled as a low-rank sparse decomposition problem; secondly, considering that the echo signal usually contains noise in the actual situation, a noise variable is introduced into the model, and based on the orthogonal matching principle, the regularization parameter of the noise variable is adaptively updated; finally, by adopting an alternating iteration framework, the singular value decomposition, the soft threshold function and the dual ascent principle are respectively used to estimate the time-frequency representation of the echo signal of the target main body, the time-frequency representation of the echo signal of the micro-motion component and the noise power. Through simulation and actual measurement verification, the method has high separation precision and strong robustness in a noise environment, and is suitable for scenes such as radar imaging and target identification.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing, specifically relating to an adaptive method for separating the echo signals of a target body and micro-moving components, used for separating the echo signals of a target body and micro-moving components under background noise conditions. Background Technology

[0002] Any vibration or rotation of a radar target, other than translational motion, will modulate the radar echo, creating fluctuating sidebands around the target's Doppler frequency—a phenomenon known as the micro-Doppler effect. The micro-Doppler effect is a key identification feature for radar targets, providing crucial information for radar imaging, feature extraction, and target recognition. The echo signal of a non-rigid, micro-moving target is a complex, multi-component signal containing both the target body and its micro-moving components. Separating the echo signals is beneficial for processing the echo signals of the target body and micro-moving components separately, facilitating micro-movement feature extraction, target recognition, and radar imaging. Therefore, over the past decade, extensive research has focused on separating and estimating the echo signals of the target body and its micro-moving components.

[0003] Generally, the instantaneous frequencies of the echo signals from the target body and micro-moving components can be modeled as polynomial and sine functions, respectively. Techniques based on point-line duality, such as the Hough transform, inverse Jordan transform, and their extensions, have been effectively used to estimate the instantaneous frequencies of the echo signals from the target body and micro-moving components in parameter space. However, these methods typically require pre-setting the instantaneous frequency modulation model, which can lead to significant noise estimation errors when the instantaneous frequency modulation model of the processed echo signal is irregular. Furthermore, various mode decomposition techniques, including local mean decomposition, empirical mode decomposition, and variational mode decomposition, have been applied to eliminate micro-Doppler components in the returned signals. Since the signals processed by radar are complex, mode decomposition techniques suitable for complex processing, such as complex local mean decomposition, complex empirical mode decomposition, and bivariate variational mode decomposition, can separate complex signals with high accuracy. However, mode decomposition methods typically require pre-setting parameters, such as the number of signal components and the center frequency. Moreover, since these methods mainly rely on frequency domain filtering, their performance is limited by the accuracy of the frequency domain filter. Compared to the frequency domain, micro-Doppler is more pronounced in the time-frequency domain. Common time-frequency transformation methods such as short-time Fourier transform and wavelet transform have been proven to effectively suppress the micro-Doppler effect of targets. Post-processing techniques based on sequence statistics, such as L-statistics and histogram analysis, have also been used to extract echo signals from micro-moving targets. However, these methods are limited by the resolution of the time-frequency analysis methods used. In recent years, super-resolution processing techniques based on sparse signal reconstruction and low-rank sparse matrix decomposition have made progress, including iterative hard thresholding, iterative shrinking thresholding, and robust principal component analysis (RPCA). These methods have been used to suppress the micro-Doppler effect in ISAR imaging, but they are mostly applied to processing broadband signals.

[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] This invention provides an adaptive method for separating the echo signals of the target body and the micro-moving parts. It aims to solve the technical problems of traditional methods under narrowband radar background noise conditions, which require preset models / parameters, are limited by the accuracy of frequency domain filters or the resolution of time-frequency analysis, have low separation accuracy of the echo signals of the target body and the micro-moving parts, have poor adaptability to irregular instantaneous frequency modulation signals, and are mostly applicable to broadband signals.

[0006] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0007] According to a first aspect of the present invention, a method for adaptively separating echo signals of a target body and a micro-moving component is provided, the method comprising: Acquire the narrowband radar echo signal of the target, the echo signal including the target body echo signal, the micro-movement component echo signal and the noise signal; Perform time-frequency transformation on the echo signal to obtain the corresponding time-frequency representation matrix; Based on the time-frequency characterization matrix, a signal decomposition model is constructed that includes a low-rank matrix, a sparse matrix, and a noise matrix, wherein the low-rank matrix corresponds to the time-frequency characterization of the target body echo signal, and the sparse matrix corresponds to the time-frequency characterization of the micro-movement component echo signal. An adaptively updated regularization parameter is introduced into the signal decomposition model to estimate the power of the noise matrix; An alternating iterative optimization framework is used to solve the signal decomposition model, and estimates of the low-rank matrix, the sparse matrix, and the noise matrix are obtained respectively, thereby separating the echo signal of the target body and the echo signal of the micro-movement component.

[0008] In some exemplary implementations, the time-domain echo signal is converted into a time-frequency representation matrix by a short-time Fourier transform.

[0009] In some exemplary embodiments, the problem of separating the target body from the echo signal of the micro-movement component is modeled as a low-rank sparse decomposition problem as follows: in, The time-frequency representation of the echo signal of the target entity. The time-frequency characterization of the echo signal from the micro-motion component. Indicates noise. Represents the inverse short-time Fourier matrix. The rank function represents the operation of calculating the rank of a matrix. Represents the 0 norm, Representing the Frobenius norm, For regularization parameters, This is the regularization parameter.

[0010] In some exemplary embodiments, the low-rank sparse decomposition problem is solved by relaxation, using the kernel norm instead of the rank function and the L1 norm instead of the L0 norm, resulting in the following solvable convex optimization problem: in Represents the nuclear norm operation. It represents the 1-norm.

[0011] In some exemplary embodiments, an adaptively updated regularization parameter is introduced into the signal decomposition model, specifically: Using the augmented Lagrangian method, the convex optimization problem can be formulated as follows:

[0012] in Representing the Lagrange multipliers, For penalty parameters, Indicates the inner product.

[0013] In some exemplary implementations, the regularization parameters of the noise variables are adaptively updated based on the orthogonal matching principle and the fixed-point iteration method, specifically as follows: Based on the orthogonal matching principle, it is assumed that the noise is orthogonal to the remaining signal after noise removal, i.e. ,in This represents the remaining signal after noise removal; By combining the formula for solving the noise estimate, the regularization parameter is derived. Iterative update formula Where k is the iteration counter, This is the conjugate transpose.

[0014] In some exemplary embodiments, the alternating iterative optimization framework is constructed based on the augmented Lagrange method and the alternating direction multiplier method; in each iteration, the estimates of the low-rank matrix, the sparse matrix, and the noise matrix are updated sequentially; wherein, the low-rank matrix is ​​solved by the singular value thresholding operator, the sparse matrix is ​​solved by the soft thresholding function, and the noise matrix is ​​solved by the dual ascent principle.

[0015] In some exemplary embodiments, the termination condition of the alternating iterative optimization process is that the relative error between two adjacent iterations is less than a preset threshold, wherein the preset threshold is less than 10. -5 .

[0016] In some exemplary embodiments, the method further includes performing an inverse short-time Fourier transform on the separated time-frequency representation to convert the echo signals of the main body and micro-motion components in the time-frequency domain back to the time domain, thereby obtaining the final time-domain target main body echo signal and micro-motion component echo signal.

[0017] The adaptive method for separating the echo signals of the target body and the micro-moving parts provided by the embodiments of the present invention has the following advantages compared with the prior art: 1. Adaptable to narrowband radar and requires no pre-set complex models: This method specifically addresses the echo separation problem of narrowband radar, eliminating the drawbacks of traditional methods that require pre-setting parameters such as instantaneous frequency modulation models, number of signal components, and center frequency. It can also effectively process echo signals with irregular instantaneous frequency modulation, significantly reducing estimation errors caused by model pre-setting, and has a wider range of applicable scenarios.

[0018] 2. Strong noise robustness and high separation accuracy: By introducing noise variables and adaptively updating the noise regularization parameters based on the orthogonal matching principle and fixed-point iteration method, the noise power can be accurately estimated and background noise interference can be effectively eliminated. Compared with traditional algorithms such as 3b-ADMM, it can separate the target body and the echo signal of the micro-moving parts with higher accuracy in noisy environments. The separation effect is significant as verified by actual measurement and simulation.

[0019] 3. Breakthrough in performance bottlenecks of traditional methods: It avoids the problems of mode decomposition methods relying on frequency domain filtering and being limited by filter accuracy, and also solves the defects of traditional time-frequency analysis methods that are limited by resolution. It utilizes the characteristics of low-rank echo of the target body and sparse echo of micro-movement parts to construct a low-rank sparse decomposition model, and combines it with the 3b-ADMM method to solve the sub-problems, which greatly improves the accuracy and stability of signal separation.

[0020] 4. High efficiency and computational reliability of iterative optimization: An alternating iterative framework is designed and a strict relative error termination condition (less than 10) is set. -5 By employing precise solution methods such as singular value thresholding and soft thresholding, the results are iteratively optimized to effectively avoid iteration errors, ensure the convergence of the calculation process and the reliability of the solution results, and stably output high-quality echo signals from the main body and micro-movement components.

[0021] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0022] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0023] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a diagram of an alternating iterative framework; Figure 3 This is the pseudocode for the method of the present invention; Figure 4 The results of processing simulation signals using different methods are shown in the figure. Figure 5 This is a schematic diagram showing the experimental setup for the method of the present invention; Figure 6 This is a diagram showing the results of processing the measured signal using the method of the present invention. Detailed Implementation

[0024] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0025] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0026] Inspired by low-rank sparse matrix factorization methods, this invention proposes an adaptive method for separating the echoes of target subjects and micro-moving components based on noise power estimation for narrowband radar data. When a target moves at a constant speed, its motion can be considered uniform motion within the coherent accumulation time. The Hankel matrix corresponding to the echo of a uniformly moving target has low-rank characteristics. This allows us to transform the problem of separating the echoes of target subjects and micro-moving components detected by narrowband radar into a low-rank decomposition problem. Since radar echoes often contain noise, we introduce additional variables into the model to account for noise energy, and adaptively update the regularization parameters of the noise variables based on a fixed-point iteration method, solving the problem within an alternating iteration framework. Simulation and empirical data analysis show that the proposed method can extract the echo signals of target subjects and micro-moving components with high accuracy in noisy environments.

[0027] refer to Figure 1 As shown, the specific steps may include: Step 1: Construct the mathematical model and matrix form of the target echo signal, model the echo signal separation problem as a low-rank sparse decomposition LRSD problem and reconstruct it into a solvable convex optimization problem; Step 2: The convex optimization problem is transformed into an augmented Lagrangian form using the augmented Lagrangian method. The subproblems are separated using the 3b-ADMM method, and the time-frequency characterization of the target body echo signal, the time-frequency characterization of the micro-movement component echo signal, and the noise estimate are obtained by solving them respectively. Step 3: Based on the orthogonal matching principle and the fixed-point iteration method, the regularization parameter of the noise variable is adaptively updated. The above solution results are iteratively optimized through an alternating iteration framework until the preset termination condition is met, and finally the separation of the echo signal of the target body and the micro-movement component is achieved.

[0028] The steps in this exemplary embodiment will now be described in more detail with reference to the accompanying drawings and embodiments.

[0029] Step 1: When the radar carrier frequency operates in the high-frequency range and the target size is within the optical range, describing the target using a point scattering model is valid. The target's echo signal can be represented as the superposition of the echoes from the target body and its micro-moving components, i.e. (1) in The echo signal representing the target entity, The echo signal representing the micro-motion component. This represents additive white Gaussian noise. Since the echo signal from the micro-moving component is a typical non-stationary signal, it can be projected into the time-frequency domain, which better observes the characteristics of non-stationary signals, using common time-frequency analysis. The short-time Fourier transform is a linear time-frequency analysis without cross-terms; the short-time Fourier transform of the target echo signal can be expressed as... (2) in Represents the Gaussian window function. The width of the window is represented. The short-time matrix of maximum overlap is equivalent to the Hankel matrix, and equation (2) can be transformed into matrix form. (3) in, For the matrix form of the window function, , For diagonalization operation, For target echo signal Time-frequency representation after short-time Fourier transform, This is a partial Fourier transform matrix, containing columns 1 to L of the complete Fourier transform matrix. echo signal of the target The short-time matrix form of the maximum overlap rate can be expressed as: (4) Based on the above analysis, the matrix form of equation (1) can be expressed as follows: (5) in , and Represent , and The short-time matrix form of the maximum overlap rate, since the short-time Fourier transform is a linear transform, is used for the time-frequency characterization of the target echo signal. It can be represented as (6) in and Represent and Time-frequency representation after short-time Fourier transform. Inverse short-time Fourier matrix. , This is a pseudo-inverse matrix operation. Generally, the target can be considered to be moving at approximately a constant velocity during the coherent accumulation time. Therefore, the target's echo signal only contains signals with a fixed Doppler frequency. According to the properties of the Hankel matrix, the Hankel matrix of the target's echo signal... It has low-rank properties. Because... According to the properties of matrix multiplication, we can obtain (7) Equation (7) shows the time-frequency characterization of the target body's echo signal. It is rank-insensitive, while the time-frequency representation of the micro-motion component echo signal is sparsity. Therefore, the problem of separating the target body from the micro-motion component echo signal can be modeled as an LRSD problem. (8) in The rank function represents the operation of calculating the rank of a matrix. Represents the 0 norm, Representing the Frobenius norm, this project's standard function is used to estimate noise. power, For regularization parameters, Here is the regularization parameter. Since the problem described by equation (8) involves the calculation of the 10-norm and rank, it is difficult to solve directly. A common approach is to replace the 0-norm with the 1-norm and the rank function with the nuclear norm. Therefore, problem (8) can be reconstructed as follows: (9) in Represents the nuclear norm operation. This represents the 1-norm. Due to noise... The power cannot be known a priori, so the regularization parameters need to be updated adaptively. To estimate noise power Regularization parameters and noise power Since they are coupled and not independent, an alternating iterative framework should be designed to solve the problem alternately, such as... Figure 2 As shown, ADMM is used in each iteration to solve for the time-frequency representation of the target body's echo signal. Time-frequency characterization of echo signals from micro-moving components and noise In the alternating iterative framework, the problem described by equation (9) can be decomposed into the following subproblems, wherek This is an iteration counter.

[0030] Step 2: Using the augmented Lagrangian method, the optimization problem described by equation (9) can be expressed as follows: (10) in Representing the Lagrange multipliers, For penalty parameters, Let represent the inner product. The problem represented by equation (10) can be restructured as follows: (11) This convex optimization problem involves , and The three main variables can be solved using the 3b-ADMM method. The optimization problem in equation (11) can be decomposed into the following sub-problems: (12) Time-frequency representation of the target subject This can be obtained by solving the following problem. (13) Problem (13) involves kernel canonical constraints and can be solved using the singular value thresholding operator. The solution can be expressed as: (14) Among them, the singular value thresholding operator , It is a soft thresholding function. This is used to obtain the time-frequency characterization of the echo signal from the micro-motion component. The objective function can be simplified to a L1 regularization problem. (15) The solution to this problem can be derived by employing a soft thresholding method. (16) To estimate the signal noise, the objective function can be expressed as: (17) Along Finding the partial derivative, it can be expressed as (18) in For the conjugate transpose. Setting equation (18) to 0, the solution for the noise can be expressed as (19) Step 3: Since the noise and signal are orthogonal, inspired by the orthogonal matching principle, we can assume... (20) in This represents the remaining signal after noise removal. Based on the above discussion, noise can be represented as... (twenty one) in It is about The function can be represented as (twenty two) Based on the fixed-point iteration method, substituting equation (22) into equation (20) yields the following formula. (twenty three) in Based on equation (22), equation (24) can be rewritten as (twenty four) Under normal circumstances Regularization parameters The value will be gradually reduced in the iterative algorithm until a specific termination condition is met. The pseudocode for the adaptive method of separating the target body from the echo signal of the micro-moving component is as follows: Figure 3 As shown, to avoid introducing iteration error, the relative error... It should be set to less than 10 -5 The value. Generally, a larger value... Values ​​that produce sparser results. Extensive experiments show that the proposed method achieves optimal performance when set between 0.01 and 0.04. The value is set to .

[0031] Figure 4 To process the results of simulation signals using different methods, such as Figure 4 As can be seen, compared with the 3b-ADMM algorithm, the proposed method can effectively separate the echo signals of the main body and the micro-moving parts, and effectively eliminate background noise. To further verify the proposed method, a principle experiment was conducted in a microwave anechoic chamber. Figure 5 This is the experimental scenario. Figure 6 The results of the proposed method on the processed measured signals are as follows: Figure 6 As shown, the proposed method can effectively process noisy measured signals.

[0032] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0033] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

[0034] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined only by the appended claims.

Claims

1. A method for adaptively separating the echo signals of a target body and a micro-moving component, characterized in that, The method includes: Acquire the narrowband radar echo signal of the target, the echo signal including the target body echo signal, the micro-movement component echo signal and the noise signal; Perform time-frequency transformation on the echo signal to obtain the corresponding time-frequency representation matrix; Based on the time-frequency characterization matrix, a signal decomposition model is constructed that includes a low-rank matrix, a sparse matrix, and a noise matrix, wherein the low-rank matrix corresponds to the time-frequency characterization of the target body echo signal, and the sparse matrix corresponds to the time-frequency characterization of the micro-movement component echo signal. An adaptively updated regularization parameter is introduced into the signal decomposition model to estimate the power of the noise matrix; An alternating iterative optimization framework is used to solve the signal decomposition model, and estimates of the low-rank matrix, the sparse matrix, and the noise matrix are obtained respectively, thereby separating the echo signal of the target body and the echo signal of the micro-movement component.

2. The method according to claim 1, characterized in that, The time-domain echo signal is converted into a time-frequency representation matrix by short-time Fourier transform.

3. The method according to claim 1, characterized in that, The problem of separating the echo signals of the target body from the micro-movement components is modeled as a low-rank sparse decomposition problem as follows: in, The time-frequency representation of the echo signal of the target entity. The time-frequency characterization of the echo signal from the micro-motion component. Indicates noise. Represents the inverse short-time Fourier matrix. The rank function represents the operation of calculating the rank of a matrix. Represents the 0 norm, Representing the Frobenius norm, For regularization parameters, This is the regularization parameter.

4. The method according to claim 3, characterized in that, By relaxing the solution of the low-rank sparse decomposition problem, replacing the rank function with the nuclear norm, and replacing the L0 norm with the L1 norm, the following solvable convex optimization problem is obtained: in Represents the nuclear norm operation. It represents the 1-norm.

5. The method according to claim 4, characterized in that, An adaptively updated regularization parameter is introduced into the signal decomposition model, specifically as follows: Using the augmented Lagrangian method, the convex optimization problem can be formulated as follows: in Representing the Lagrange multipliers, For penalty parameters, Indicates the inner product.

6. The method according to claim 5, characterized in that, The regularization parameters of the noise variables are adaptively updated based on the orthogonal matching principle and the fixed-point iteration method, specifically as follows: Based on the orthogonal matching principle, it is assumed that the noise is orthogonal to the remaining signal after noise removal, i.e. ,in This represents the remaining signal after noise removal; By combining the formula for solving the noise estimate, the regularization parameter is derived. Iterative update formula Where k is the iteration counter, This is the conjugate transpose.

7. The method according to claim 1, characterized in that, The alternating iterative optimization framework is constructed based on the augmented Lagrange method and the alternating direction multiplier method. In each iteration, the estimated values ​​of the low-rank matrix, sparse matrix and noise matrix are updated sequentially. The low-rank matrix is ​​solved by the singular value thresholding operator, the sparse matrix is ​​solved by the soft thresholding function, and the noise matrix is ​​solved by the dual ascent principle.

8. The method according to claim 7, characterized in that, The termination condition for the alternating iterative optimization process is that the relative error between two adjacent iterations is less than a preset threshold, where the preset threshold is less than 10. -5 .

9. The method according to claim 1, characterized in that, The method further includes performing an inverse short-time Fourier transform on the separated time-frequency representation to convert the echo signals of the main body and micro-movement components in the time-frequency domain back to the time domain, thereby obtaining the final time-domain echo signals of the target main body and micro-movement components.

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